Is my cousin considered legally accountable (mukallaf shar'an), given that he is 13 years old and only has pubic hair, without having experienced nocturnal emission (ihtilam) or shown other signs of puberty?

The jurists differed on whether the growth of pubic hair is a sign of puberty, holding three opinions:

The First Opinion: It is not a sign at all. This is the view of Abu Hanifa and a narration from Malik. The Second Opinion: It is always a sign. This is the doctrine of the Malikis and Hanbalis, and a narration from Abu Yusuf. They cited the hadith of the Prophet, peace and blessings be upon him, regarding Banu Qurayza, and the actions of the Companions as evidence. The Third Opinion: It is a sign in some cases but not others. This is the view of the Shafi'is and some Malikis. The Shafi'is consider it a sign of puberty for the child of a disbeliever and for one whose Islam is unknown, but not for a Muslim male or female. Some Malikis, on the other hand, believe it is a sign in apparent rulings between a person and others.

The coarse hair is considered what is meant by growth as a sign of puberty, not the fine, downy hair.